Penalty/finite-element approximations of a class of unilateral problems in linear elasticity

The present paper is concerned with a development of a penalty/finite-element approximation of a class of unilateral problems in linear elasticity. A penalty method is applied to resolve the inequality constraint due to contact, and convergence with respect to the penalty parameter is discussed. Then finite-element approximations are introduced to the penalized formulation with a priori error estimates in terms of the penalty and mesh parameters. Several numerical examples are also given in the end of the paper.